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Annals of Global Analysis and Geometry

, Volume 46, Issue 3, pp 241–257 | Cite as

Classification of Möbius homogenous surfaces in \({\mathbb {S}}^4\)

  • Changping Wang
  • Zhenxiao XieEmail author
Article

Abstract

A surface \(M^2\) in \(\mathbb {S}^4\) is called Möbius homogeneous if for any two points \(p,q \in M^2\) there exists a Moebius transformation which takes \(p\) to \(q\) and keeps \(M^2\) invariant. In this paper we give a complete classification of the Möbius homogenous surfaces in \(\mathbb {S}^4\).

Keywords

Moduli space Möbius invariant Conformal Gauss Map  Möbius homogenous surface 

Mathematics Subject Classification (2000)

53A30 53A55 53C42 

Notes

Acknowledgments

This work is funded by the Project 11171004 and 11331002 of National Natural Science Foundation of China. We thank Professor Haizhong Li and Professor Faen Wu for the helpful discussions and valuable advices.

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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.School of Mathematics and Computer ScienceFujian Normal UniversityFuzhouPeople’s Republic of China
  2. 2.School of Mathematical SciencesPeking UniversityBeijingPeople’s Republic of China

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